Cat allergy?

So my son has been getting over a cold for about a week now. A family member had something come up where they had to get rid of a couple kittens and I have mentioned on here before about him being obsessed and wanting to get him one. So we took in them in. My son has been sneezing, coughing, runny nose before from school and now around one of his eyes is red. This appeared 3 days after we got the kittens. Mostly likely a cat allergy? Or maybe apart of his cold? I’m so sad over this he loves his new kittens. I just have no experience with cats or anyone being allergic.